3. Geometry & Trigonometry

The Geometry & Trigonometry topic has twice as much content at the HL level (51 suggested teaching hrs) than the SL level (25 suggested teaching hrs) because there is no vectors content at the SL level.

∼ quick link ∼
exercise sets, quizzes & tests for teaching units in Geometry & Trig

10 Feb 2021: New trigonometry unit test that can be used with SL and/or HL students and full worked solutions has been posted: AA_SLHL_Test1_trig

Changes compared to previous Maths HL-SL syllabusses:
As mentioned above, the most significant change is that vectors is only at HL level. Thus, at SL level it is expected that when a student is required to determine the measure of an angle it wil always involve the use of right triangle trigonometry. The only other change is the addition of the following content in syllabus item SL 3.1*: volume and surface area of 3D solids including right pyramid, right cone, sphere, hemisphere and combinations of these solids.

Geometry & Trigonometry - syllabus overview

Syllabus item numbers are in brackets.

SL - Geometry & Trig

SL core (AA & AI)

3D geometry (3.1)

triangle trigonometry & applications (3.2, 3.3)


angles, circles, arcs & sectors (3.4)

trig functions, equations & identities (3.5 - 3.8)

sine rule – ambiguous case (3.5)

HL - Geometry & Trig


further trig functions, identities & properties (3.9 - 3.11)

vector basics (3.12)

scalar product & applications (3.13)

vectors – equations of lines (3.14, 3.15)

vector product & applications (3.16)

lines and planes in space (3.17, 3.18)

 Exercise Sets, Quizzes & Tests

Set of six questions covering trigonometry content from syllabus item 3.2 to 3.8.  No GDC on Qs 1-4; GDC allowed on Qs 5 & 6. The syllabus content is appropriate for both SL and HL students.  Worked solutions are included on the 2nd page.

Trigonometry test covering the following syllabus items: using trigonometric ratios to find sides and angles of right-angled triangles; area of triangle; area of sector; angles of elevation & depression; sine rule (including ambiguous case); cosine rule; use of bearings; angle between a line and a plane. Solution key (worked solutions) available below.

Solution key (worked solutions) for SL trigonometry test above.

Trigonometry unit test that can be used with SL and/or HL students. Questions 1-7 for SL students (40 marks), and Qs 1-9 for HL students (50 marks). Questions 8 & 9 are good 'discriminating' questions for HL students; that is, students for which HL is too challenging will usually not do well on Qs 8 & 9. Solution key (worked solutions) available below.

Solution key (worked solutions) for SL-HL trigonometry unit test above.

Selected Pages

Triangle trig & applications 23 March 2021

A large portion of the Geometry & Trigonometry syllabus topic (especially SL) focuse on trigonometry - and a large portion...

Trig functions, equations & identities 20 January 2021

The trigonometry syllabus content can essentially be split into two parts (with some overlap) of triangle trigonometry and...

Vectors HL 18 November 2020

go to unit tests on vectors below ↴Comparing the syllabus content on vectors for the 'new' Analysis & Approaches course...

Ambiguous case (side-side-angle SSA) 16 June 2020

When learning the effective application of the Law of Sines and Cosine Rule, it is essential that students understand (which...

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